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CTET Paper I (Classes I to V) 30 Jan 2023 Solved Paper

Question : 47 of 150

Marks: +1, -0

What is the sum of all the factors of 56 ?

Solution:

Concept:

The sum of all factors of a number is found by writing it as a product of primes, then using the formula: (sum of powers of each prime) multiplied together.

Explanation:

First, factorize 56 into primes:

56 = 2 \times 2 \times 2 \times 7 = 2^3 \times 7^1

Then, apply the sum formula:

(2^0 + 2^1 + 2^2 + 2^3) \times (7^0 + 7^1)

Calculate each part:

1 + 2 + 4 + 8 = 15

and

1 + 7 = 8

Multiply:

15 \times 8 = 120

Thus, the sum of all factors of 56 is 120.

Answer:

B. 120

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